The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.
Questions tagged [moment-of-inertia]
912 questions
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Toilet paper dilemma
There are two ways to orient the toilet paper: "over" (left image), "under" (right image).
Each has it's pros and cons. For some reason, it's always easier to tear off the paper in the "over" orientation even though we apply the same force thus…
Monopole
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Do black holes have a moment of inertia?
My question is in the title: Do black holes have a moment of inertia?
I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the literature.
mattiav27
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Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)?
Why is the moment of inertia (wrt. the center) for a hollow sphere higher than a solid sphere (with same radius and mass)? I have completely no idea and I am inquiring about this as it is an interesting question that popped in my head while doing…
Jossie
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How many types of inertia are there?
I was looking for types of inertia, but I am confused. My book says there are three types of inertia, namely inertia of rest, inertia of motion, and inertia of direction. But when I searched for these types in good books like Halliday, Randall,…
Shinnaaan
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Why certain rotations are unstable? (Euler Equations)
We have the Euler equations for a rotating body as follows
$$I_1\dot\omega_1+\omega_2\omega_3(I_3-I_2)=0\\
I_2\dot\omega_2+\omega_1\omega_3(I_1-I_3)=0\\
I_3\dot\omega_3+\omega_2\omega_1(I_2-I_1)=0$$
Where $I_i$ are the moments of inertia about the…
John Doe
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Distinguishing between solid spheres and hollow spheres (equal mass)
If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment.
What's the best way(s) to recognize the hollow sphere and solid sphere?
Berne
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Can the direction of angular momentum and angular velocity differ?
While studying rotational mechanics, I came across a section where it mentioned that angular momentum may not necessarily be parallel to angular velocity. My thoughts were as follows:
Angular momentum ($L$) has the relation $L=I\omega$ where…
Physicsapproval
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What is the physical significance of the off-diagonal moment of inertia matrix elements?
The tensor of moment of inertia contains six off-diagonal matrix elements, which vanish if we choose a reference frame aligned with the principal axes of the rotating rigid body; the angular momentum vector is then parallel to the angular velocity.…
noir1993
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What's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional case, we have a matrix (i.e. moment of inertia…
user1285419
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Is there a quantum analogue of the "Tennis Racket" theorem?
A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is unstable. This is known as the "tennis racket"…
KF Gauss
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Why do non-rigid bodies try to increase their moment of inertia?
I have oft noticed that a non-rigid body on being rotated tries to increase its moment of inertia.
Is there any way we can prove this in a logical and mathematical fashion?
Suhrid Mulay
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Why does a cuboid spin stably around two axes but not the third?
Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$.
Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, one passing through the centers of the $a$–$b$ faces, one…
Mark Dominus
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Do higher-order mass moments have any physical meaning?
The zeroth moment of mass of an object is simply its total mass.
The first moment of mass yields an object's center of gravity (after normalization).
The second moment of mass yields an object's moment of inertia.
Is there an analogous physical…
David Zhang
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Why doesn't this way of calculating the moment of inertia of a sphere work?
Instead of the usual approach of integrating a bunch of discs, I do it differently. I integrate by subdividing the sphere into a bunch of concentric spheres containing mass on their surface.
The integral becomes:
$\int_0^R r^2 \cdot (4\pi r^2) \cdot…
user2714980
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Does a rotating rod have both translational and rotational kinetic energy?
I've recently learned about rotational kinetic energy and how an object can have both translational kinetic energy and rotational kinetic energy at the same time.
However, I get confused when I try to apply this to, say, a uniform rod rotating…
Christopher Miller
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